Future work: Our study combined with the literature study on the classical model (REF ) by [1]}, [2]}, [3]}, [4]}, [5]}, provide us a better understanding on how different dispersal behavior of predator could have different effects on the dynamical outcomes and spatial pattens. In nature, predator may have different foraging behavior as pointed out by [6]} that the foraging movements of predator Coccinellids are combinations of passive diffusion, conspecific attraction, and retention on plants with high aphid numbers. It will be interesting to the extended version of Model (REF ) and Model (REF ) by incorporating two different modes of foraging behavior. One potential example is showed as follows:
\(\begin{aligned}\frac{dx_1}{dt} & = x_1\left(1 - \frac{x_1}{K_1}\right) - \frac{a_1 x_1 y_1}{1 + x_1} \\\frac{dy_1}{dt} & = \frac{a_1 x_1 y_1}{1 + x_1} -d_1 y_1+ \rho _1\textbf {s}\left( \frac{a_1 x_1 y_1}{1 + x_1} y_2- \frac{a_2 x_2 y_2}{1 + x_2} y_1\right)+\rho _1\textbf {(1-s)}\left( y_2-y_1\right)\\\frac{dx_2}{dt} & = r x_2\left(1 - \frac{x_2}{K_2}\right) - \frac{a_2 x_2 y_2}{1 + x_2} \\\frac{dy_2}{dt} & = \frac{a_2 x_2 y_2}{1 + x_2} -d_2 y_2+\rho _2\textbf {s}\left( \frac{a_2 x_2 y_2}{1 + x_2} y_1- \frac{a_1 x_1 y_1}{1 + x_1} y_2\right)+\rho _2\textbf {(1-s)}\left( y_1-y_2\right)\end{aligned}\) 
